How to select part of a mesh by using a helper plane?
1. Lasso Select:

You can use Lasso Select with Ctrl + LMB.



Here a related Post for types of selection.

Limit selection to visible should be disabled to select all vertices in the Lasso area.


Image by iKlsR♦ answer





2. Object as Camera:

This solution involves a 2nd Object which is perpendecular to the Plane and use it as a Camera. That makes it easier for a Border Selection and the 3D Cursor is used for the orientation.




Position the Plane at the desired Location.
Dublicate the Plane with Shift + D in Object Mode
Rotate the duplicated Plane by 90° around the local X-axis. R + 2xX + 90
Translate the rotated Plane along the local Z-axis with G + 2xZ.



Select the first Plane and press Shift + S > Cursor to Selected.
Select the second Plane and press Ctrl + Numpad 0 to make the Plane the active Camera.
Select your Object, toggle to Edit Mode and Border Select B the desired Vertices. The 3D Cursor helps where to stop with the selection.


Vertices selection successfully